We compute the dynamical evolution of hierarchical triple stars in which both orbits are initially circular, and determine the lower limit to the ratio of periods (outer/inner) for which there is dynamical stability. This ranges from 6.3 to 2.4, as the distant body's mass (in units of the inner binary) ranges from 100 to 0.01. We discuss a variety of types of behaviour that we find when the period ratio varies near its critical value.
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Kiseleva et al. (1994) studied this question.